Abstract. A surveillance-evasion differential game of degree with a detection zone in the shape of a two-dimensional cone is posed. The nature of the optimal strategies and the singular phenomena of the value function are described and correlated to subsets of the space of all possible parameter combinations, showing the relation of the singular phenomena in differential game theory and control theory.
Abstract. The game of degree is analyzed in a surveillanceevasion problem: the evader strives to escape as soon as possible from the pursuer's detection circle, while the pursuer's desire is the opposite. The evader moves with constant speed and is capable of instantaneous direction changes. The pursuer has a minimum turn-radius, independent of speed, and can move forward with any speed not exceeding a maximum greater than the evader's speed.The solution is surprisingly complex, including regions where the pursuer's speed is optional, switch envelopes, focal lines, as well as chattering by the pursuer to prevent the crossing of certain barriers.
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